The average arithmetic mean of the integers from 200 to 400 is 300.
Explanation
When dealing with a sequence of consecutive integers, the arithmetic mean (average) can be found using a simple formula. This is because the numbers are evenly spaced.
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Understanding Arithmetic Mean: The arithmetic mean is the sum of a collection of numbers divided by the count of numbers in the collection.
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Evenly Spaced Integers: In this case, we have integers from 200 to 400. This forms an evenly spaced set.
Calculation
According to the provided reference, for an evenly spaced set of integers, the average is calculated as:
(First Number + Last Number) / 2
Applying this to our problem:
(200 + 400) / 2 = 600 / 2 = 300
Therefore, the average arithmetic mean of the integers from 200 to 400 is 300.
Example
Let's consider a smaller range of integers, from 1 to 5.
- Integers: 1, 2, 3, 4, 5
- Sum: 1 + 2 + 3 + 4 + 5 = 15
- Count: 5
- Arithmetic Mean: 15 / 5 = 3
Using the formula (First + Last) / 2:
(1 + 5) / 2 = 6 / 2 = 3
As we can see, both methods give the same result. This confirms the validity of the formula for evenly spaced integers.
